Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology

Jarno Vanhatalo, Aki Vehtari
Gaussian Processes in Practice, PMLR 1:73-89, 2007.

Abstract

Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v1-vanhatalo07a, title = {Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology}, author = {Vanhatalo, Jarno and Vehtari, Aki}, booktitle = {Gaussian Processes in Practice}, pages = {73--89}, year = {2007}, editor = {Lawrence, Neil D. and Schwaighofer, Anton and Quiñonero Candela, Joaquin}, volume = {1}, series = {Proceedings of Machine Learning Research}, address = {Bletchley Park, UK}, month = {12--13 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v1/vanhatalo07a/vanhatalo07a.pdf}, url = {https://proceedings.mlr.press/v1/vanhatalo07a.html}, abstract = {Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.} }
Endnote
%0 Conference Paper %T Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology %A Jarno Vanhatalo %A Aki Vehtari %B Gaussian Processes in Practice %C Proceedings of Machine Learning Research %D 2007 %E Neil D. Lawrence %E Anton Schwaighofer %E Joaquin Quiñonero Candela %F pmlr-v1-vanhatalo07a %I PMLR %P 73--89 %U https://proceedings.mlr.press/v1/vanhatalo07a.html %V 1 %X Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data.
RIS
TY - CPAPER TI - Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology AU - Jarno Vanhatalo AU - Aki Vehtari BT - Gaussian Processes in Practice DA - 2007/03/11 ED - Neil D. Lawrence ED - Anton Schwaighofer ED - Joaquin Quiñonero Candela ID - pmlr-v1-vanhatalo07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 1 SP - 73 EP - 89 L1 - http://proceedings.mlr.press/v1/vanhatalo07a/vanhatalo07a.pdf UR - https://proceedings.mlr.press/v1/vanhatalo07a.html AB - Log Gaussian processes are an attractive manner to construct intensity surfaces for the purposes of spatial epidemiology. The intensity surfaces are naturally smoothed by placing a Gaussian process (GP) prior over the relative log Poisson rate, and the spatial correlations between areas can be included in an explicit and natural way into the model via a correlation function. The drawback with using a Gaussian process is the computational burden of the covariance matrix calculations. To overcome the computational limitations a number of approximations for Gaussian process have been suggested in the literature. In this work a fully independent training conditional sparse approximation is used to speed up the computations. The posterior inference is conducted using Markov chain Monte Carlo simulations and the sampling of the latent values is sped up by a transformation taking into account their posterior covariance. The sparse approximation is compared to a full GP with two sets of mortality data. ER -
APA
Vanhatalo, J. & Vehtari, A.. (2007). Sparse Log Gaussian Processes via MCMC for Spatial Epidemiology. Gaussian Processes in Practice, in Proceedings of Machine Learning Research 1:73-89 Available from https://proceedings.mlr.press/v1/vanhatalo07a.html.

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